Question: Rewrite as a simplified fraction. ${3.60\overline{6} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3606.6666...\\ 100x &= 360.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3246}$ ${x = \dfrac{3246}{900}} $ ${x = \dfrac{541}{150}} \text{or} {3 \dfrac{91}{150}}$